How to copy transform orientation to object's rotation?
I've contrived some code to do the trick. Please don't laugh on the lame-code - it works. :-) Maybe somebody will find it useful.



If you want to use it, just save the the text below as the "align_to_to_inverted.py" file, and then install it as an add-on. And you will have the "Align to Transform Orientation inverted" command in your Object menu. It's tricky to insert it in the "Object > Transform", so let's let it be there =).

To use it, in the Object mode select the source object and then the target object (if you want to copy source object's rotation), and execute the command. Selction will be reset, but the target object will remain active.

If you want to align to Transform Orientation, select the only target object, and execute the command. Note that you must set some custom transform orientation. Built in orientations, like Global, View, etc, will not do.

# align_to_to_inverted.py
# The script will align active object to selected one (if there is another selected object).
# or it will use current custom Transform Orientation (if any).
# It changes object's rotation values, but leaves its orientation intact.
# (c) LIII A.S. Mechanic Kharkov

bl_info = {
    "name": "Align to Transform Orientation inverted",
    "description": "Operator to set object's rotation as another's or current custom transform orientation.",
    "location": "Object menu",
    "version": (0, 1, 1),
    "blender": (2, 76, 0),
    "support": "COMMUNITY",
    "wiki_url": "https://blender.stackexchange.com/q/110894/23172",
    "warning": "",
    "category": "Object",
    "author" : "Mechanic. Kharkov."
}

import bpy
from mathutils import * # yes, I know

class AlignToTOInverted(bpy.types.Operator):
    """Aligns active object's rotation values only to selected or TO"""
    bl_idname = "object.align_to_to_inverted"
    bl_label = "Align to Transform Orientation inverted"
    bl_options = {'REGISTER', 'UNDO'}  # Enable undo for the operator.

    @classmethod
    def poll(cls, context):
        return context.active_object is not None

    def execute(self, context):

        trg = bpy.context.active_object
        print("trg: %s" %(trg))

        #find source object
        src = None
        for o in bpy.context.selected_objects:
            if o != trg:
                src = o
                break

        if not src:

            #try to find current user Transform Orientation
            #but this will work only in 3DVIEW space.
            mco = None
            try:
                co = bpy.context.space_data.current_orientation
                if co:
                    mco = co.matrix
                    print("Using Ttansform Oientation %s" % (co.name))
                    print("matrix= %s" % (mco))
                else:
                    print("No Ttansform Oientation found")
            except:
                mco = None

            if not mco:    
                self.report({'ERROR_INVALID_INPUT'},"No source object selected\nYou have to select two objects, or be in a custom Transform Orientation.")
                return {'CANCELLED'}

            # ger src natrix, and transposed
            msrc = mco
            trs = msrc.transposed()
            q = trs.to_quaternion()


        else:
            # source given as object
            print("Source object: %s" %(src))
            # ger src natrix, and transposed
            msrc = src.matrix_world
            trs = msrc.transposed()
            q = trs.to_quaternion()

        #now we rotate trg back to apply zero rotation
        mtrg = trg.matrix_world.copy().to_3x3()
        mtrg.rotate(q)
        mtrg = mtrg.to_4x4()
        trg.matrix_world *= mtrg
        #deselect all but trg object
        bpy.ops.object.select_all(action='TOGGLE')
        #select trg as active object
        trg.select = True
        bpy.context.scene.objects.active = trg
        #apply this as default rotation
        bpy.ops.object.transform_apply(location=False, rotation=True, scale=False)
        #and now rotate back to src rotation
        q = msrc.to_quaternion()
        mtrg = trg.matrix_world.to_3x3()
        mtrg.rotate(q)
        mtrg = mtrg.to_4x4()
        trg.matrix_world *= mtrg

        return {'FINISHED'}

def menu_func(self, context):
    self.layout.operator(
        AlignToTOInverted.bl_idname)


def register():
    bpy.utils.register_class(AlignToTOInverted)
    bpy.types.VIEW3D_MT_object.append(menu_func)


def unregister():
    bpy.utils.unregister_class(AlignToTOInverted)
    bpy.types.VIEW3D_MT_object.remove(menu_func)


# This allows you to run the script directly from Blender's Text editor
# to test the add-on without having to install it.
if __name__ == "__main__":
    register()

    # test call
    #bpy.ops.object.align_to_to_inverted()